ATK & damage
Physical damage is built from several layers: status ATK (from STR, or DEX for ranged), weapon ATK with its refine bonus, then target-size, element and card modifiers, and only then DEF is subtracted. Refine above the safe limit grants a random over-upgrade bonus.
Two parts of damage
Let us start with the core idea: when your character swings a sword, an axe, or fires a bow, the game has to decide how much HP to remove from the monster. That decision is the «physical damage». It is built from two big parts that are simply added together: status ATK (your «bare body» — damage from your character stats, mostly STR) and weapon ATK (damage from the weapon itself, plus its refine). No magic here: first we compute those two numbers, add them, and only then layer the modifiers on top.
Status ATK and the STR square
Status ATK for melee is calculated as: STR + ⌊STR/10⌋² + ⌊DEX/5⌋ + ⌊LUK/5⌋. The brackets ⌊…⌋ mean «round down» (drop the fractional part). So STR plays the leading role, while DEX and LUK add a little each. The most interesting piece is the ⌊STR/10⌋² term: it is quadratic, and that is exactly why STR is so valuable at high values. We will break it down separately below, because it is the favourite «magic trick» of veteran players.
Ranged combat: STR↔DEX
If you are a ranged attacker — bow, instrument (bard/dancer), whip, or firearm (gunslinger) — the formula is the same, but STR and DEX swap places. That means for ranged combat the main damage stat becomes DEX: DEX + ⌊DEX/10⌋² + ⌊STR/5⌋ + ⌊LUK/5⌋. This is why archers pump DEX rather than STR — for them DEX deals damage, lands hits (HIT), and speeds up casting. A very convenient stat.
Weapon ATK and refine
The second part — weapon ATK — is the weapon base ATK (shown in its description) plus the refine bonus: refine × perPlus. How much one refine gives (perPlus) depends on the weapon level (level 1–4, not to be confused with a character level requirement): a lv1 weapon gives +2 ATK per «plus», lv2 → +3, lv3 → +5, lv4 → +7. So a +10 on a lv4 weapon (axe, two-hander) is a whole +70 ATK, while on a lv1 dagger it is only +20. On top of that, refining beyond the «safe limit» (where there is already a chance to break the weapon) also grants a random over-upgrade bonus on top — a small but pleasant extra.
Modifier order and cards
Once we have status ATK + weapon ATK, the game applies modifiers in a strict order: first the size multiplier of the target (different weapons hit small/medium/large differently), then masteries and skill damage are added, next a crit check (×1.4 and it fully ignores DEF!), then the target DEF is subtracted, then the element multiplier, and finally — cards. Remember this rule about cards: cards of the same category (for example, two «+20% damage vs Demi-Human») add up (+40%), while cards of different categories multiply. It is precisely this multiplication that lets a stack of different-type cards reach those insane numbers in end-game builds.
statusATK = STR + floor(STR/10)² + floor(DEX/5) + floor(LUK/5)- STR
- character STR stat
- DEX
- character DEX stat
- LUK
- character LUK stat
weaponATK = baseATK + refine × perPlus (perPlus: lv1 +2, lv2 +3, lv3 +5, lv4 +7)- baseATK
- weapon base ATK (from item DB)
- refine
- weapon refine level (+0…+10)
damage = (statusATK + weaponATK) × sizeMod × elementMod × cards − DEF- sizeMod
- weapon × target-size modifier (table)
- elementMod
- attack element vs defense element modifier
| Status ATK | 90 + ⌊90/10⌋² + ⌊40/5⌋ + ⌊20/5⌋ | 183 |
| Refine bonus | 4 × 7 (lv4) | +28 |
| Weapon ATK | 120 + 28 | 148 |
| Size modifier | axe × Large | ×1.00 |
| Element modifier | Neutral → Fire | ×1.00 |
| Damage before DEF | 183 + 148 (до DEF) | 331 |
Imagine a Swordman: STR 90, DEX 30, LUK 10, melee (sword). We plug into the formula STR + ⌊STR/10⌋² + ⌊DEX/5⌋ + ⌊LUK/5⌋:STR → 90⌊90/10⌋² = 9² = 81 (there it is, the quadratic term!)⌊30/5⌋ = 6⌊10/5⌋ = 2Sum: 90 + 81 + 6 + 2 = 179 status ATK — and that is still without any weapon. Notice that almost half came from a single quadratic term (81 out of 179). That is exactly why STR is not a «linear» stat.
Take two weapons with the same base ATK 120, both refined to +9.lv4 sword (perPlus = 7): weapon ATK = 120 + 9×7 = 120 + 63 = 183lv1 dagger (perPlus = 2): weapon ATK = 120 + 9×2 = 120 + 18 = 138A whole 45 ATK difference just from the weapon level! That is why, all else being equal, players pick a higher-level weapon to refine. Plus, beyond the safe limit a random over-upgrade bonus kicks in, so the real numbers at +10/+11 can be a touch higher still.
Let us put it all together. Status ATK 179 (from the example above) + weapon ATK 138 (dagger +9) = 317 «raw» ATK. We hit a large monster (Large), but a dagger vs Large hits for only 50% (size). The attack element is neutral against the target — a 100% multiplier.317 × 0.50 (size) × 1.00 (element) = ≈158 before subtracting DEF. If the target has soft DEF 20, the final is ≈ 138. Now imagine you grabbed an axe (vs Large — 100%): the same character would deal ≈317 × 1.00 = twice as much. This is why choosing a weapon to match the target size is no small thing.
- Because of the quadratic term ⌊STR/10⌋², the main STR «thresholds» are every round multiple of ten: 40, 50, 60, …, 90, 100. It is exactly when you cross a ten that the square jumps:STR 89 → ⌊89/10⌋² = 8² = 64; STR 90 → 9² = 81 — one point adds +17 to the term.STR 99 → 9² = 81; STR 100 → 10² = 100 — one point adds +19! That is why 99 vs 100 STR is the classic «sweet» breakpoint in builds that have stat bonuses.Practical takeaway: when you spend points, try to «round up» STR to a multiple of ten (counting job/food/buff bonuses), because points inside a ten (say, 91…99) scale almost linearly, while crossing a ten gives that quadratic jump. For ranged combat it is all the same, just count the thresholds by DEX (49→50, 99→100, and so on).
- Confusing weapon level with a level requirement. «lv4 weapon» is not «wearable from level 4» — it is the weapon class (1–4) that determines the refine perPlus. A two-handed axe is a typical lv4.An archer pumping STR. For bow/instrument/whip/firearm the main damage stat is DEX, because the formula swaps STR↔DEX. An archer barely needs STR (only for weight).Ignoring target size. A dagger vs Large is only 50%. If you grind a field of large mobs with a dagger, you are voluntarily cutting half your damage.Thinking crit «pierces everything equally». Crit gives ×1.4 and ignores DEF, but it triggers BEFORE the DEF subtraction in the calculation order — and it does not cancel element/size.Adding cards of different categories. Two «+20% vs Demi-Human» give +40% (addition within a category), but «+20% vs Demi-Human» × «+20% vs Brute» is multiplication, not +40%.Underestimating the quadratic term. Players often think «+10 STR = +10 ATK». At high STR, crossing a ten gives far more thanks to ⌊STR/10⌋².
Formulas verified against the uAthena engine (pre-renewal, Episode 11.2).